Gaussian Copula Joint Models for Mixed Longitudinal (k, l)-Inflated Conway–Maxwell Poisson and Continuous Responses

Abstract

In this paper, we propose joint model for claim counts and amounts in non-life insurance using a Gaussian Copula joint model for analyzing longitudinal (k, l)-inflated Conway–Maxwell Poisson and Normal responses with random effects. We develop a Gaussian Copula-based regression model that accounts for associations between count responses which are inflated in two points. Our approach utilizes underlying latent variables to reveal the hidden mechanisms that produce count responses, particularly in cases where some of these responses exhibit inflation at two specific points. The Gaussian Copula approach are used to investigate both of the correlation between mixed responses and the correlation of longitudinal nature. The full likelihood-based inference method is applied for the estimation of parameters to obtain maximum likelihood estimates of the parameters. To illustrate the utility of the models, some simulations are illustrated. A simulation study is performed in which for count response (k, l)-Inflated Conway–Maxwell Poisson and distributions are considered. Finally, the proposed models are applied to real-life insurance data, specifically an Iranian automobile insurance dataset, which exhibits overdispersion and is derived from an observational study.